If I was going to do a Google Phishing page - I would take the username + password that the user supplied into MY fake page, and POST/CURL that to the Google login.
If Google returns asking for a 2factor to MY fake, I would display the 2 factor prompt to the user, and get them to type the 2-factor into my page, which I would pass back to Google.
Basically you can use a phishing page as a MITM attack.
When you auth against Google with 2-factor, there is a "remember this computer" option - giving the attacker at least 30 days of access to your email without needing a further 2-factor code.
So if the person is tricked enough to type their username+password into a fake google page, they are just as likely to follow through with their 2-factor code.